A microwave realization of the chiral GOE

Ulrich Kuhl
Institut de Physique de Nice (INPHYNI), CNRS, Universite de Cote d'Azur

The universal features of the spectra of chaotic systems are well reproduced by the corresponding quantities of the random matrix ensembles [1]. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles: the Gaussian orthogonal (GOE), the Gaussian unitary (GUE), and the Gaussian symplectic ensemble (GSE). With a further particle-antiparticle symmetry there are in addition the chiral variants of these ensembles [2]. Relativistic quantum mechanics is not needed to realize the latter symmetry. A tight-binding system made up of two subsystems with only interactions between the subsystems but no internal interactions, such as a graphene lattice with only nearest neighbor interactions, will do it as well. First results of a microwave realization of the chiral GOE (the BDI in Cartan's notation) will be presented, where the tight-binding system has been constructed by a lattice made up of dielectric cylinders [3].

[1] O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. PRL 52, 1 (1984).

[2] C. W. J. Beenakker. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

[3] S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne. Disordered graphene and boron nitride in a microwave tight-binding analog. PRB 87, 035101 (2013).